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Simplifying 2y2 + -50y + 225 = 0 Reorder the terms: 225 + -50y + 2y2 = 0 Solving 225 + -50y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 112.5 + -25y + y2 = 0 Move the constant term to the right: Add '-112.5' to each side of the equation. 112.5 + -25y + -112.5 + y2 = 0 + -112.5 Reorder the terms: 112.5 + -112.5 + -25y + y2 = 0 + -112.5 Combine like terms: 112.5 + -112.5 = 0.0 0.0 + -25y + y2 = 0 + -112.5 -25y + y2 = 0 + -112.5 Combine like terms: 0 + -112.5 = -112.5 -25y + y2 = -112.5 The y term is -25y. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25y + 156.25 + y2 = -112.5 + 156.25 Reorder the terms: 156.25 + -25y + y2 = -112.5 + 156.25 Combine like terms: -112.5 + 156.25 = 43.75 156.25 + -25y + y2 = 43.75 Factor a perfect square on the left side: (y + -12.5)(y + -12.5) = 43.75 Calculate the square root of the right side: 6.614378278 Break this problem into two subproblems by setting (y + -12.5) equal to 6.614378278 and -6.614378278.Subproblem 1
y + -12.5 = 6.614378278 Simplifying y + -12.5 = 6.614378278 Reorder the terms: -12.5 + y = 6.614378278 Solving -12.5 + y = 6.614378278 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + y = 6.614378278 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + y = 6.614378278 + 12.5 y = 6.614378278 + 12.5 Combine like terms: 6.614378278 + 12.5 = 19.114378278 y = 19.114378278 Simplifying y = 19.114378278Subproblem 2
y + -12.5 = -6.614378278 Simplifying y + -12.5 = -6.614378278 Reorder the terms: -12.5 + y = -6.614378278 Solving -12.5 + y = -6.614378278 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + y = -6.614378278 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + y = -6.614378278 + 12.5 y = -6.614378278 + 12.5 Combine like terms: -6.614378278 + 12.5 = 5.885621722 y = 5.885621722 Simplifying y = 5.885621722Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.114378278, 5.885621722}
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